CAT 2025 Formula Sheet PDF: All Important Quantitative Aptitude Formulas for Quick Revision

CAT 2025 Formula Sheet PDF: All Important Quantitative Aptitude Formulas for Quick Revision

Team Careers360Updated on 07 Jan 2026, 11:22 AM IST

The CAT Formula Sheet 2026 is a crucial preparation resource for aspirants aiming to score well in the Quantitative Aptitude section of the CAT exam. It serves as a compact, easy-to-revise compilation of all important formulas from key topics such as Arithmetic, Algebra, Geometry and Mensuration, Number System, and Modern Maths. Instead of revisiting bulky notes or textbooks, candidates can rely on a formula sheet for quick concept refreshment. Regular use of the CAT Formula Sheet helps strengthen formula retention, improves calculation speed, and reduce mistakes during practice.

This Story also Contains

  1. CAT 2026 Quantitative Aptitude Formula Sheet PDF Download
  2. CAT Important Formulas of Geometry
  3. CAT Important Formulas of Trigonometry
  4. Quantitative Aptitude Formulae for CAT 2026
  5. CAT 2026 Quantitative Aptitude Cheat Sheet PDF
  6. CAT 2026 Formula Sheet: Why You Need It?
  7. Key Benefits of Using a CAT Quant Formula Sheet
  8. How to Use CAT Formula Sheet 2026 PDF?
  9. How to Memorise CAT 2026 Formulas Effectively
  10. How to Create Your CAT 2026 Formula Sheet?
  11. CAT 2026 Recommended eBooks and Study Materials
CAT 2025 Formula Sheet PDF: All Important Quantitative Aptitude Formulas for Quick Revision
CAT 2025 Formulae

In this article, you will get a free CAT 2026 Formula Sheet PDF along with chapter-wise important Quant formulas, shortcuts, and tips for quick revision.

CAT 2026 Quantitative Aptitude Formula Sheet PDF Download

Download the CAT 2026 formula PDF designed for fast revision and last-minute preparation. This free formula sheet covers all the important formulae that will be helpful to solve questions quickly in the CAT exam.

Download Now: CAT 2026 Important Formulas

CAT Important Formulas of Geometry

Mastering important geometry formulas is crucial for cracking the CAT exam, as geometry is a key topic in the Quantitative Aptitude section. The following section covers all essential CAT geometry formulas, including areas, polygons, angles, and properties of triangles and circles to help you solve problems quickly and accurately.

Topic

Formula

Area of Triangle

$\frac{1}{2} \times \text{Base} \times \text{Height}$

Heron's Formula

$A = \sqrt{s(s-a)(s-b)(s-c)};; s = a + b + c$

Pythagoras Theorem

$a^2 + b^2 = c^2\ \text{(for right-angled triangle)}$

Equilateral Triangle Area

$3a^2$

Circumference of Circle

$2\pi r$

Area of Circle

$\pi r^2$

Length of Arc

$\dfrac{\theta}{360^{\circ}} \times 2\pi r$

Area of Sector

$\dfrac{\theta}{360^{\circ}} \times \pi r^2$

Area of Rectangle

$L \times B$

Perimeter of Rectangle

$2(L+B)$

Area of Square

$a^2$

Perimeter of Square

$4a$

Area of Parallelogram

$\text{Base} \times \text{Height}$

Area of Rhombus

$\dfrac{1}{2} d_1 d_2$

Sum of Interior Angles

$(n-2) \times 180^\circ$

Each Interior Angle (Regular Polygon)

$\dfrac{(n-2) \times 180^\circ}{n}$

Each Exterior Angle (Regular Polygon)

$\dfrac{360^\circ}{n}$

Surface Area of Sphere

$4\pi r^2$

Volume of Sphere

$\dfrac{4}{3}\pi r^3$

Surface Area of Cylinder

$2\pi r(h+r)$

Volume of Cylinder

$\pi r^2 h$

Surface Area of Cone

$\pi r(r+l)$

Volume of Cone

$\dfrac{1}{3}\pi r^2 h$

CAT Important Formulas of Trigonometry

Trigonometry plays a vital role in the CAT Quantitative Aptitude section, making it essential to learn and memorise key formulas. This comprehensive list of important CAT trigonometry formulas helps aspirants solve complex problems with speed, accuracy, and confidence during the exam.

1. Basic Trigonometric Ratios

These are defined in relation to a right-angled triangle:

$\sin \theta = \frac{\text{Opposite side}}{\text{Hypotenuse}}$

$\cos \theta = \frac{\text{Adjacent side}}{\text{Hypotenuse}}$

$\tan \theta = \frac{\text{Opposite side}}{\text{Adjacent side}}$

$\csc \theta = \frac{\text{Hypotenuse}}{\text{Opposite side}}$

$\sec \theta = \frac{\text{Hypotenuse}}{\text{Adjacent side}}$

$\cot \theta = \frac{\text{Adjacent side}}{\text{Opposite side}}$

2. Pythagorean Identities

$\sin^2 \theta + \cos^2 \theta = 1$

$1 + \tan^2 \theta = \sec^2 \theta$

$1 + \cot^2 \theta = \csc^2 \theta$

3. Trigonometric Functions of Negative Angles

$\sin(-\theta) = -\sin \theta$

$\cos(-\theta) = \cos \theta$

$\tan(-\theta) = -\tan \theta$

$\csc(-\theta) = -\csc \theta$

$\sec(-\theta) = \sec \theta$

$\cot(-\theta) = -\cot \theta$

4. Angle Sum and Difference Formulas

$\sin(A + B) = \sin A \cos B + \cos A \sin B$

$\sin(A - B) = \sin A \cos B - \cos A \sin B$

$\cos(A + B) = \cos A \cos B - \sin A \sin B$

$\cos(A - B) = \cos A \cos B + \sin A \sin B$

$\tan(A + B) = \frac{\tan A + \tan B}{1 - \tan A \tan B}$

$\tan(A - B) = \frac{\tan A - \tan B}{1 + \tan A \tan B}$

Quantitative Aptitude Formulae for CAT 2026

Quantitative Aptitude formulas form the foundation of the Quantitative Aptitude section in the CAT 2026 exam. Here are some important CAT 2026 quant section-wise formulae for CAT 2026 preparation:

Arithmetic

The Arithmetic section is the most important section in the Quantitative Aptitude Section, which is also useful to solve the Data Interpretation problems. Following are some 50+ Important Formulas for CAT Preparation of this section which are given in this CAT Formula Sheet:

Percentage

Following are some Important CAT Formulas of percentage:

$X \text{ is what percentage of } Y = \frac{X}{Y} \times 100$

$X \text{ is what percentage more/less than } Y = \frac{|X - Y|}{Y} \times 100$

Shortcut Formulas

Following are some formulas which can be used as CAT Quant Formulae:

Concept

Formula

Successive percentage change

Overall

Changes in A when B and C are altered

Overall

Price increase followed by a decrease

Overall

Profit & Loss:

Following are some Important CAT Formulas of this topic:

Concept

Formula

Selling Price and Profit

$S.P. = C.P. + \text{Profit}$

Selling Price and Loss

$S.P. = C.P. - \text{Loss}$

Profit or Loss Percentage

$\text{Profit or Loss Percentage}$

Discount Percentage

$\text{Discount Percentage}$

Selling Price with Profit or Loss

$S.P. = \frac{C.P. \times 100 + \text{Profit} \times 100}{100}$

Selling Price with Profit or Loss

$S.P. = \frac{C.P. \times 100 - \text{Loss} \times 100}{100}$

Simple Interest (S.I.) & Compound Interest (C.I.):

Following are some basic and Important Formulas for CAT 2026 related to Simple Interest and Compound Interest:

Concept

Formula

Simple Interest

For Principal ($P$), Rate of Interest ($R$), Time ($T$):

$S.I. = P \times R \times T / 100$

Compound Interest (annually)

$A = P(1 + \dfrac{R}{100})^n$

where $n$ = time in years.

Compound Interest (half-yearly)

$A = P \left(1 + \dfrac{R}{2 \times 100}\right)^{2T}$

Total Amount

$A = P + \text{Interest}$

Shortcut Formulas

Following are some formulas which can be used as CAT Quant Formula Cheat Sheet for the preparation and exam point of view:

Concept

Formula

Doubling Time with Compound Interest

Time to double = $\dfrac{72}{R}$ years

(where $R$ = annual interest rate)

Difference Between C.I. and S.I. (2 years)

$C.I. - S.I. = P \left( \dfrac{R}{100} \right)^2$

Difference Between C.I. and S.I. (3 years)

$C.I. - S.I. = P \left( \dfrac{R}{100} \right)^2 \left( 3 + \dfrac{R}{100} \right)$

Time, Speed & Distance:

Following are some basic and Important Formulas for CAT 2026 related to Time, Speed and Distance:

Concept

Formula

Distance

$D = S \times T$

Average Speed

$\text{Average Speed} = \dfrac{\text{Total Distance}}{\text{Total Time}}$

Trains:

Concept

Formula

Time for a train to cross a pole/person

$T = \dfrac{l}{s}$

Where: $l =$ Length of the train, $s =$ Speed of the train

Time for a train to cross a platform/tunnel

$T = \dfrac{l + d}{s}$

Where: $l =$ Length of the train, $d =$ Length of platform/tunnel, $s =$ Speed of the train

Time for trains to cross each other (same direction)

$T = \dfrac{l_1 + l_2}{s_1 - s_2}$

Where: $l_1, l_2 =$ Lengths of Train 1 and Train 2; $s_1, s_2 =$ Speeds of Train 1 and Train 2

Time for trains to cross each other (opposite direction)

$T = \dfrac{l_1 + l_2}{s_1 + s_2}$

Where: $l_1, l_2 =$ Lengths of Train 1 and Train 2; $s_1, s_2 =$ Speeds of Train 1 and Train 2

Boat & Streams:

Concept

Formula

Speed of Boat in Still Water

$x$ kmph

Speed of Stream/Water/Current

$y$ kmph

Travelling Time

$t$ hr

Distance (Downstream: same direction)

$D = (x + y) \times t$ km

Distance (Upstream: opposite direction)

$D = (x - y) \times t$ km

Clocks

Concept

Formula

Speed of Hour Hand

$0.5^\circ$ per minute

Round covered by Hour Hand

$1$ round $= 360^\circ$ in $12$ hours or $720$ minutes

Speed of Minute Hand

$6^\circ$ per minute

Round covered by Minute Hand

$1$ round $= 360^\circ$ in $1$ hour or $60$ minutes

Angle between Hour and Minute Hands

$\theta =|\frac{11}{2}M-30H$|

Shortcut Formulas

We have provided below the shortcut formulae related to average speeds, boat stream, circular tracks, meeting point, to make your calculations faster in the CAT 2026 exam.

1. Average Speed Formulas

Case 1: Equal distances, different speeds
If the distance covered in each stage of a journey is the same, but speeds are different, the average speed is the harmonic mean:

$ \text{Average Speed} = \frac{2 s_1 s_2}{s_1 + s_2} $

Example:
Distance from A to B and B to C is the same. Speeds: $s_1$ and $s_2$. Then:

$ \text{Average Speed} = \frac{2 s_1 s_2}{s_1 + s_2} $

Case 2: Equal time, different speeds
If the time taken in each stage is the same but speeds differ, the average speed is the arithmetic mean:

$ \text{Average Speed} = \frac{s_1 + s_2}{2} $

2. Circular Track – Same Direction

If two people start from the same point on a circular track of length $D$ km with speeds $a$ & $b$ kmph in the same direction:

  1. Time for first meeting:

$ t_{\text{first}} = \frac{D}{|a-b|} $

  1. Time to meet again at the starting point:

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$ t_{\text{start}} = \text{LCM}\left(\frac{D}{a}, \frac{D}{b}\right) $

  1. Number of distinct meeting points:

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$ \text{Meeting points} = |x - y| $

Where $x:y$ is the simplified ratio of speeds.
Example: If $a = 12$ kmph, $b = 9$ kmph → $x:y = 12:9 = 4:3$ → $x=4$, $y=3$.

3. Circular Track – Opposite Direction

If two people start from the same point in opposite directions:

  1. Time for first meeting:

$ t_{\text{first}} = \frac{D}{a+b} $

  1. Time to meet again at the starting point:

$ t_{\text{start}} = \text{LCM}\left(\frac{D}{a}, \frac{D}{b}\right) $

  1. Number of distinct meeting points:

$ \text{Meeting points} = |x + y| $

Where $x:y$ is the simplified ratio of speeds.

4. Meeting Point Between Two Opposite Travellers

If a person $P$ starts from $A$ towards $B$, and $Q$ starts from $B$ towards $A$, and they meet after time $t$:

$ t = x \cdot y $

Where:

  • $x$ = time taken by $P$ to reach $B$ after meeting

  • $y$ = time taken by $Q$ to reach $A$ after meeting

5. Boats and Streams

If the speed of the boat downstream is $u$ kmph and upstream is $v$ kmph:

  • Speed of boat in still water:

$ \text{Boat speed} = \frac{u+v}{2} \text{ kmph} $

  • Rate of stream:

$ \text{Stream speed} = \frac{u-v}{2} \text{ kmph} $

Geometry

The Geometry section is the lengthiest section in the Quantitative Aptitude Section which has lots of properties and formulas. Following are 50+ Important Formulas for CAT Preparation of this section which are given in this CAT Formula Sheet:

1. Triangles:

Properties of Triangles:

The sum of all interior angles in a triangle is $180^\circ$ and the sum of all exterior angles is $360^\circ$.

The sum of any two sides is always greater than the third one and the difference of any two sides is less than the third one.

Let $a, b, c$ be the sides of a triangle, then

$|b-c| < a < b+c$

In a scalene triangle the greatest side is always greater than one-third of the perimeter and less than half of the perimeter.

Let $a, b, c$ be the sides of the triangle and $a$ be the greatest side. Let the perimeter be $P$. Then

$\dfrac{P}{3} < a < \dfrac{P}{2}$

Example: In a scalene triangle $ABC$, the perimeter is $24$ cm and all sides are integers.

Let $a, b, c$ be sides of the triangle with $a$ the greatest side. Then

$\dfrac{24}{3} < a < \dfrac{24}{2}$

$8 < a < 12$

So possible values are $9, 10, 11$ cm.

For $a, b, c$ sides of a triangle and $a$ the greatest side:

If $a^2 < b^2 + c^2$, then the triangle is acute angled.

If $a^2 = b^2 + c^2$, then the triangle is right angled (Pythagoras theorem).

If $a^2 > b^2 + c^2$, then the triangle is obtuse angled.

(Here $D$ is the midpoint of side $AC$, so $AD = DC$)

Mid point of triangle

Midpoint of a triangle

  • Length of the Median –
    BD = $\frac12 \sqrt{2(AB^2+BC^2)−AC^2}$

  • 3× (Sum of squares of sides) =4× (Sum of squares of medians), that is,
    $3(a^2+b^2+c^2)=4({M_a}^2+{M_b}^2+{M_c}^2)$
    where a,b, and c are the sides of the triangle and Ma, Mb, and Mc are the medians.

  • In a right-angled triangle, Median of Hypotenuse = Half of Hypotenuse
    That is,
    CD = AB/2

median of hypotenuse

Median of the hypotenuse

If all the medians are drawn in the triangle, then the 6 small triangles are generated in the triangle, which are equal in the Area.

Area of Triangle:

Heron’s Formula

If all sides of a triangle are given. Let $a, b, c$ be the sides of the triangle –

Area $= \sqrt{s(s-a)(s-b)(s-c)}$ where $s = \dfrac{a+b+c}{2}$ is the semiperimeter.

If two sides and the included angle are given –

Area $= \dfrac{1}{2} \times \text{(Product of given sides)} \times \sin(\text{included angle})$

Area $= \dfrac{1}{2} \times a \times b \times \sin C$

(Example: sides $a, b$ and included angle $C$ are given)

If a side and its respective altitude (perpendicular drawn from the opposite vertex) is given, then –

Area of the triangle $= \dfrac{1}{2} \times \text{Base} \times \text{Height (Altitude)}$

Shortcut Formulas

Area of an equilateral triangle = $ \frac{\sqrt{3}}{4} a^2 $

Height (Altitude) of an equilateral triangle = $ \frac{\sqrt{3}}{2} a $

Area of a triangle = $ r \times s $ (where $r$ is the inradius and $s$ is the semiperimeter)

Area of a triangle = $ \frac{abc}{4R} $ (where $a$, $b$, $c$ are sides and $R$ is the circumradius)

Quadrilaterals:

Trapezium

Trapezium

Area: $ \frac{1}{2} \times (\text{Sum of Parallel Sides}) \times \text{Height} $
$ \frac{1}{2} \times (AB + CD) \times H $

Parallelogram

Parallelogram

Opposite angles and sides are equal.
Diagonals bisect each other.
Sum of squares of diagonals: $ 2(a^2 + b^2) $
Area: $ \text{Base} \times \text{Height} = a \times h $
Area (with angle): $ a \cdot b \cdot \sin \theta $

Rhombus

Rhombus



All sides and opposite angles are equal.

Diagonals bisect each other at 90∘.

Sum of squares of diagonals: $ 4a^2 $
Area: $ \frac{1}{2} d_1 d_2 $
Perimeter: $ 4a $

Where:
a is the length of a side,
d1 and d2 are the lengths of the diagonals.

Rectangle

Perimeter: $ 2(l + b) $ (where $l =$ length, $b =$ breadth)
Area: $ l \times b $
Length of diagonal: $ \sqrt{l^2 + b^2} $

Square

Perimeter: $ 4a $ (where $a =$ side of square)
Area: $ a^2 $
Length of diagonal: $ a\sqrt{2} $

Cyclic Quadrilateral

Cyclic Quadrilateral

$\text{Sum of opposite angles} = 180^\circ$

$\text{Area} = \frac{1}{2} \times d_1 \times d_2 \times \sin \theta \quad \text{(where } \theta \text{ is the angle between the diagonals)}$

$\text{Area} = (s - a)(s - b)(s - c)(s - d), \quad \text{where } a,b,c,d \text{ are sides and } s = \frac{a + b + c + d}{2} \text{ is the semi-perimeter}.$

3. Circle:

Circumference of a circle $= 2\pi r$

Area of a circle $= \pi r^2$

For a semi-circle:

Circumference of a semi-circle $= \pi r$

Perimeter of a semi-circle $= \pi r + 2r$

Area of a semi-circle $= \dfrac{\pi r^2}{2}$

Sector & Segment of a circle

Sector of circle

$OAXC$ is called the sector of the circle and $AXC$ is called the segment.

Length of arc $AXC = \dfrac{\theta}{360} \times 2\pi r$ (where $r$ is the radius)

Area of sector $OAXC = \dfrac{\theta}{360} \times \pi r^2$

$2 \times \text{Area of sector} = \text{Length of arc} \times \text{Radius}$

Area of segment $AXC = \text{Area of sector } OAXC - \text{Area of } \triangle OAC$

$A = \dfrac{\theta}{360} \pi r^2 - \dfrac{1}{2} r^2 \sin \theta$

Where:

$\theta$ = angle subtended at the center (in degrees)

$r$ = radius of the circle

Common Tangent

$PQ$ and $RS$ are the direct common tangents of the circles, which are equal in length.

Length of direct common tangent $(L)$:

$L^2 = d^2 - (r_1 - r_2)^2$

Where:

$d =$ distance between centers of the circles

$r_1, r_2 =$ radii of the circles

Direct common tangent

$PQ$ and $RS$ are the transverse common tangents of the circles, which are equal in length.

Length of transverse common tangent $(L)$:

$L^2 = d^2 - (r_1 + r_2)^2$

Where:

$L =$ length of the transverse common tangent

$d =$ distance between the centers of the two circles

$r_1, r_2 =$ radii of the two circles

TRANSVERSE COMMON TANGENT

Mensuration:

Cube

{a- side of cube}

Let a be the side of the cube:

  • Lateral Surface Area (L.S.A.): $ 4a^2 $

  • Total Surface Area (T.S.A.): $ 6a^2 $

  • Volume: $ a^3 $

Cuboid

{l-length, b-breadth,

h-height}

Let l = length, b = breadth, h = height:

  • Lateral Surface Area (L.S.A.): $ 2(l + b)h $

  • Total Surface Area (T.S.A.): $ 2(lb + bh + hl) $

  • Volume: $ l \times b \times h $

Cylinder

{r-radius of circular base,

h-height}

Let r = radius of base, h = height:

  • Curved Surface Area (C.S.A.): $ 2\pi r h $

  • Total Surface Area (T.S.A.): $ 2\pi r (r + h) $

  • Volume: $ \pi r^2 h $

Cone

{r-radius of circular base,

h-height, l- slant height}

Curved Surface Area (C.S.A.): $ \pi r l $

Total Surface Area (T.S.A.): $ \pi r (r + l) $

Volume: $ \frac{1}{3}\pi r^2 h $

Where:
r = radius,
h = height,
l = slant height

Sphere

{r-radius}

Total Surface Area: $ 4\pi r^2 $

Volume: $ \frac{4}{3} \pi r^3 $

Where r is the radius.

Hemi-sphere

{r-radius}

Let r be the radius:

  • Curved Surface Area (C.S.A.): $ 2\pi r^2 $

  • Total Surface Area (T.S.A.): $ 3\pi r^2 $

  • Volume: $ \frac{2}{3} \pi r^3 $

Algebra

The Algebra section is a critical part of the Quantitative Aptitude section in the CAT exam. Below are over 50 important formulas for CAT preparation in this section, which are provided in this comprehensive CAT Formula Sheet:

1. Quadratic Equations

General form:
$ ax^2 + bx + c = 0 $

Roots of the equation (Shreedhara Acharya's Formula):
$ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $

Sum of roots:
$ \text{Sum} = -\frac{b}{a} $

Product of roots:
$ \text{Product} = \frac{c}{a} $

Discriminant:
$ D = b^2 - 4ac $

  • If $D > 0$, roots are real and distinct


    • Perfect square $D$ → roots are rational (e.g., $x=1,6$)

    • Non-perfect square $D$ → roots are irrational/conjugate surds (e.g., $x = 3 - \sqrt{5}, 3 + \sqrt{5}$)

  • If $D = 0$, roots are real and equal

  • If $D < 0$, roots are imaginary and distinct

Vertex (Maximum/Minimum values):

  • For $y = ax^2 + bx + c$, $a>0$ (Minimum):
    $ x = -\frac{b}{2a}, \quad y_{\text{min}} = -\frac{D}{4a} $

  • For $y = ax^2 + bx + c$, $a<0$ (Maximum):
    $ x = -\frac{b}{2a}, \quad y_{\text{max}} = -\frac{D}{4a} $

Quadratic equation from roots $a$ and $b$:
$ x^2 - Sx + P = 0 $, where $ S = a+b $, $ P = ab $
Or equivalently:
$ x^2 - (a+b)x + ab = 0 $

Progression & Series

Arithmetic Progression (A.P.)

If a is the first term and d is the common difference then the Arithmetic Progression (A.P.). can be written as-

  • a, a+d, a+2d, a+3d, …

Let $a =$ first term

$d =$ common difference

$n$ = number of terms

Nth term of the A.P. –

$T_n = a + (n-1)d$

Sum of the first $n$ terms of the A.P. $(S_n)$ = Average of all the terms $\times$ number of terms $(n)$.

The average of the terms can be found easily:

If the number of terms is odd, then the middle term will be the average.

Example: $2, 5, 8, 11, 14$ are terms of the A.P., then the middle term $8$ is the average.

So, $S_n = \text{average} \times n = 8 \times 5 = 40$.

If the number of terms is even, then the average of the middle two terms will be the average of the A.P.

Formula for the sum of $n$ terms:

$S_n = \dfrac{n}{2} \big[ 2a + (n-1)d \big]$

Shortcut Formulae

$S_n = \dfrac{n}{2}(a+l)$ (where $a =$ first term, $l =$ last term, $n =$ number of terms)

$n = \dfrac{l-a}{d}+1$ (number of terms in A.P.)

Geometric Progression (G.P.)

If $a$ is the first term and $r$ is the common ratio, then the G.P. can be written as: $a, ar, ar^2, ar^3, \dots$

Nth term of the G.P.: $T_n = a \cdot r^{n-1}$

Sum of the first $n$ terms:

If $|r| < 1$: $S_n = a \cdot \dfrac{1-r^n}{1-r}$

If $r > 1$: $S_n = a \cdot \dfrac{r^n-1}{r-1}$

Sum of infinite terms of the G.P. (if $|r|<1$): $S_\infty = \dfrac{a}{1-r}$

Where: $a =$ first term, $r =$ common ratio, $n =$ number of terms

$|r|<1$ ensures the series converges.

Shortcut Formulas

If there are odd no. of terms in a G.P., then the product of all terms are equal to the nth power of the middle term.

e.g. 2,6,18,54,162 are the terms of a G.P.

Then the products of all the terms = 185

Harmonic Progression (H.P.)

If a,b,c are in A.P., then $\frac{1}{a},\frac{1}{b},\frac{1}{c}$ are in Harmonic Progression (H.P.).

n-th term of the H.P.=$\frac{1}{n}$-th term of the corresponding A.P.

Series

Sum of first $n$ natural numbers:
$ 1 + 2 + 3 + \cdots + n = \frac{n(n+1)}{2} $

Sum of squares of first $n$ natural numbers:
$ 1^2 + 2^2 + 3^2 + \cdots + n^2 = \frac{n(n+1)(2n+1)}{6} $

Sum of cubes of first $n$ natural numbers:
$ 1^3 + 2^3 + 3^3 + \cdots + n^3 = \left(\frac{n(n+1)}{2}\right)^2 $

Sum of first $n$ odd numbers:
$ 1 + 3 + 5 + \cdots + (2n-1) = n^2 $

Sum of squares of first $n$ even numbers:
$ 2^2 + 4^2 + 6^2 + \cdots + (2n)^2 = \frac{2n(n+1)(2n+1)}{3} $

Sum of squares of first $n$ odd numbers:
$ 1^2 + 3^2 + 5^2 + \cdots + (2n-1)^2 = \frac{n(2n+1)(2n-1)}{3} $

Indices & Surds

Product Rule:
$ a^m \cdot a^n = a^{m+n} $

Quotient Rule:
$ \frac{a^m}{a^n} = a^{m-n} $

Power of a Power:
$ (a^m)^n = a^{mn} $

Power of a Product:
$ (ab)^n = a^n \cdot b^n $

Power of a Quotient:
$ \left(\frac{a}{b}\right)^n = \frac{a^n}{b^n} $

Negative Exponent:
$ a^{-n} = \frac{1}{a^n} $

Shortcut Formulae

Infinite Product: $\prod_{n=1}^{\infty} a_n = \lim_{n \to \infty} \prod_{k=1}^{n} a_k$

Logarithmic Rules and Properties

Definition of Logarithm:
$ \log_b a = x ;;\Longleftrightarrow;; b^x = a $

Log of 1:
$ \log_b 1 = 0 \quad (b>0, ; b \neq 1) $

Log of the base itself:
$ \log_b b = 1 $

Log of a product:
$ \log_b (mn) = \log_b m + \log_b n $

Log of a quotient:
$ \log_b \left(\frac{m}{n}\right) = \log_b m - \log_b n $

Log of a power:
$ \log_b (m^n) = n \cdot \log_b m $

Change of base formula:
$ \log_b a = \frac{\log_k a}{\log_k b} $

Base switch rule:
$ \log_a b = \frac{1}{\log_b a} $

CAT 2026 Quantitative Aptitude Cheat Sheet PDF

The CAT 2026 Quantitative Aptitude Cheat Sheet PDF is a compact, high-utility resource covering all essential formulas, theorems, and shortcuts from Arithmetic, Algebra, Geometry, Modern Math, and Number Systems. It’s designed for rapid revision and accuracy improvement during mock tests. Students can quickly recall percentage-to-ratio conversions, time–speed–distance relationships, and equation-solving tricks. The CAT Quant formula sheet PDF also includes sectional difficulty markers and formula interlinks to help identify topic dependencies. Thus, it helps in last-minute prep and stronger conceptual recall during the CAT QA section.

Download Now: CAT 2026 Quantitative Aptitude Cheat Sheet PDF

CAT 2026 Formula Sheet: Why You Need It?

A CAT 2026 formula sheet acts as a quick reference guide during preparation. It helps you recall key concepts, save revision time, and improve accuracy in problem-solving. Having all important formulas from Arithmetic, Algebra, Geometry, and Modern Math in one place boosts your speed and confidence while attempting Quantitative Aptitude questions in the exam.

Saves Time During CAT Revision

A well-organised CAT formula sheet allows you to revise important concepts quickly before mocks and the final exam. Instead of searching through multiple books or notes, you can go through one sheet that covers all crucial formulas from Arithmetic, Algebra, Geometry, and Numbers. This structured revision helps you improve speed and problem-solving efficiency.

Strengthens Conceptual Clarity

Preparing a formula sheet for CAT 2026 preparation builds a stronger understanding of topics. Writing and categorising formulas by section—like percentages, ratios, or permutations—helps you connect ideas and recall the right one during tough questions. This approach ensures both clarity and application accuracy in the actual exam.

Minimises Errors and Improves Accuracy

Many students make small calculation errors due to confusion between similar formulas. Regularly revising from your CAT Quant formula sheet helps you retain correct equations and avoid mix-ups. Clear understanding of formula derivations enhances precision, reducing the chances of negative marking in the test.

Enhances Mock Test Performance

Using a CAT formula sheet during mock test practice can significantly improve your score. Reviewing it before and after each mock boosts memory retention and highlights weak areas. You can track which formulas you forget often and revise them again—turning your mock analysis into a more effective learning process.

Builds Confidence Before the Exam

Before appearing for CAT 2026, revising all key formulas from your sheet gives a psychological advantage. It helps calm nerves, refresh memory, and strengthen exam confidence. A personalised, well-maintained formula sheet acts like a final preparation guide, ensuring you enter the exam hall fully prepared.

Key Benefits of Using a CAT Quant Formula Sheet

A CAT Quant formula sheet is one of the smartest ways to simplify exam preparation. It helps you revise essential formulas, identify weak areas, and boost problem-solving speed. With quick access to all important concepts, aspirants can focus better, reduce last-minute stress, and improve their CAT 2026 Quantitative Aptitude performance significantly.

Simplifies Formula Revision

The CAT 2026 Quant formula sheet collects all key formulas in one place—covering Arithmetic, Algebra, Geometry, and Modern Math. Instead of flipping through books, you can revise every crucial concept quickly. This saves time and helps maintain consistent practice, ensuring you remember formulas even under exam pressure.

Improves Calculation Speed

Remembering formulas accurately is essential for speed-based exams like CAT 2026. Regular revision from your Quant formula sheet helps you apply equations faster, solve complex problems efficiently, and attempt more questions in less time. This habit can make a major difference in your sectional and overall percentile.

Boosts Accuracy and Reduces Errors

A personalised CAT Quant formula sheet strengthens your recall and clarity. When you know which formula fits each question type, you reduce silly mistakes and confusion. Repeatedly reviewing and testing yourself on these formulas improves accuracy, especially in topics like Time-Speed-Distance, Profit-Loss, and Probability.

Supports Last-Minute Preparation

During the final days before CAT 2026, revising entire books isn’t practical. Your Quant formula sheet becomes the ultimate quick revision guide. It helps you brush up on important equations and shortcuts in a few hours, keeping your memory fresh right before the exam.

Helps Identify Weak Areas

While updating your CAT 2026 Quantitative Aptitude formula sheet, you’ll naturally notice which topics you often skip or forget. This helps in analysing your weaker areas early and focusing your preparation accordingly. Over time, it turns into a powerful self-assessment and improvement tool for CAT aspirants.

How to Use CAT Formula Sheet 2026 PDF?

Using a CAT Formula Sheet 2026 PDF the right way can significantly improve Quantitative Aptitude performance and overall CAT score. A well-organised formula sheet supports fast revision, strengthens concept retention, and reduces calculation errors during CAT mock tests and the final exam. Instead of rote learning, aspirants should use the CAT formula PDF as a tool for concept application, exam strategy building, and time management aligned with CAT 2026 syllabus and pattern.

Use the Formula Sheet for Practice

Use the CAT formula sheet PDF before starting practice sessions to refresh key formulas and concepts from Arithmetic, Algebra, Geometry, and Number System. After practice, revisit the sheet to connect formulas with solved questions, improving conceptual clarity and retention.

Apply Formulas to CAT Previous Year Questions

Practising CAT previous year questions alongside the formula sheet helps identify high-frequency formulas and common application patterns. This builds familiarity with exam-level questions and improves formula selection speed during the actual CAT exam.

CAT Mock Test Analysis

Keep the CAT formula sheet handy while analysing full-length and sectional mock tests. Highlight mistakes caused by incorrect formula usage or forgotten concepts and update the PDF with short reminders, making it more exam-oriented.

Revise Topic-Wise CAT Formulas

Use the CAT formula sheet PDF for topic-wise revision, especially in weak sections such as percentages, time and work, or mensuration. Focused revision improves accuracy and boosts confidence in low-scoring areas.

Practice Instead of Passive Reading

Avoid repeatedly reading the CAT formula PDF 2026. Instead, practise active recall by writing formulas from memory or explaining them aloud. This technique strengthens long-term memory and improves recall under exam pressure.

Use the Formula Sheet for Final CAT 2026 Revision

In the last phase of CAT 2026 preparation, rely on your concise CAT formula sheet PDF for quick daily revision. It saves time, enhances speed, and ensures all important formulas remain fresh before the exam.

How to Memorise CAT 2026 Formulas Effectively

The CAT 2026 Quantitative Aptitude section tests both accuracy and speed. Since most questions rely on direct formula application, mastering and retaining formulas from Arithmetic, Algebra, Geometry, Modern Math, and Number Systems is crucial. Using smart memorisation techniques like spaced repetition, topic clustering, and visual recall helps improve long-term retention and boosts problem-solving efficiency during mocks and the actual CAT exam.

Use Spaced Repetition for Formula Retention

Spaced repetition helps strengthen memory through periodic reviews. Use digital tools like Anki or Notion flashcards to revise formulas at increasing intervals—1 day, 3 days, 7 days, and 15 days. This scientifically proven method ensures that key CAT Quant formulas (like simple and compound interest, quadratic roots, and geometry area relations) stay fresh and accessible during timed tests.

Create Topic-Wise Formula Sheets

Divide formulas by topic, Arithmetic (Percentages, Ratios, Averages), Algebra (Equations, Inequalities), Geometry (Circles, Triangles, Mensuration)—and maintain a concise sheet for each. This topic-wise segregation improves focused revision and pattern recognition, making it easier to recall related concepts together during CAT 2026 QA problem-solving. Keep each sheet concise with examples and shortcut notes for quick scanning.

Apply Formulas Through Daily Practice Questions

Retention improves when formulas are applied regularly. Practice 5–10 formula-based questions daily from mock papers or sectional tests. For instance, when revising Time–Speed–Distance, solve both basic and mixed-level problems to understand contextual application. Continuous exposure helps bridge the gap between theoretical knowledge and practical problem-solving during CAT’s high-pressure environment.

Use Mnemonics and Visual Memory Aids

Visual learning techniques improve recall under exam stress. Create mind maps, flowcharts, or acronym-based mnemonics for formula clusters (like SOH–CAH–TOA for trigonometry). Use color-coded notes to differentiate between formula types—geometry in blue, algebra in green, arithmetic in red. These cues help visually trigger recall during CAT Quantitative Aptitude questions.

Revise Formulas During Mock Test Analysis

After every mock or sectional test, review formulas linked to incorrect or time-consuming questions. Maintain a Formula Revision Log that tracks which formulas caused confusion or slow recall. Revisit and reapply these during subsequent practice sessions. This iterative feedback loop ensures you don’t just memorise but also master CAT 2026 Quant formulas through active error correction.

How to Create Your CAT 2026 Formula Sheet?

Creating a well-structured CAT 2026 formula sheet is a crucial step in strengthening Quantitative Aptitude preparation. A compact and personalised formula sheet helps in quick revision, improves formula recall, and boosts problem-solving speed during CAT mock tests. Instead of blindly memorising formulas, aspirants should focus on concept clarity, formula application, and continuous refinement based on topic-wise practice, previous year questions, and exam-level difficulty.

Organise CAT Formulas Topic-Wise

Divide your CAT Quant formula sheet into clear sections such as Arithmetic, Algebra, Geometry & Mensuration, Number System, and Modern Maths. Topic-wise organisation helps in targeted revision and prevents confusion between similar-looking formulas. This structure is especially helpful during sectional tests and last-minute preparation.

Include Only High-Frequency CAT Formulas

Focus on formulas that appear repeatedly in CAT previous year papers, such as those related to averages, percentages, ratios, time and work, profit and loss, linear and quadratic equations, and mensuration. Excluding rarely used formulas keeps your sheet concise and exam-oriented.

Add Concept-Based Usage Notes

Next to each formula, write a short explanation describing when, why, and how the formula is applied. Mention typical question patterns, assumptions, or limitations. These notes reduce errors caused by incorrect formula application under time pressure.

Maintain Shortcuts and Value Tables

Create a dedicated section for fraction-to-percentage conversions, squares, cubes, square roots, common ratios, and approximation values. These shortcuts significantly improve calculation speed, which is critical in CAT’s time-bound environment.

Update Using Mock Test Analysis

After analysing every CAT 2026 mock test, update your formula sheet by adding forgotten formulas or correcting misunderstood concepts. This continuous refinement ensures your sheet reflects real exam-level challenges and personal weak areas.

Revise Daily for Speed and Accuracy

Regular revision—preferably daily or on alternate days—helps transfer formulas into long-term memory. Consistent recall practice improves speed, accuracy, and confidence, making your CAT formula sheet a powerful last-phase revision tool.

CAT 2026 Recommended eBooks and Study Materials

Explore the best CAT 2026 eBooks and study materials recommended by experts for complete preparation. These resources will help aspirants revise efficiently and boost exam preparation.

Title Download Link

CAT 2026 Quantitative Aptitude 20 Free Sectional Tests

Download Now

CAT 2026 Arithmetic Important Concepts and Practice Questions

Download Now

CAT 2026 Algebra Important Concepts and Practice Questions

Download Now

CAT 2026 Quantitative Aptitude Study Material PDF - Geometry and Mensuration

Download Now

CAT 2026 Number System Important Concepts and Practice Questions

Download Now

CAT 2026 Quantitative Aptitude Questions with Answers PDF

Download Now


Frequently Asked Questions (FAQs)

Q: What are the most important formulas for CAT Quantitative Aptitude?
A:

Key formulas include percentages, profit and loss, time-speed-distance, averages, simple and compound interest, geometry theorems, and algebraic identities. These formulas help solve most Quant questions quickly and accurately in CAT 2025.

Q: Are NCERT books useful for CAT preparation?
A:

Yes, NCERT books, particularly for subjects like Mathematics, provide a solid foundation. They are especially beneficial for beginners to grasp basic concepts before moving to more complex materials.

Q: Which Geometry formulas are frequently used in CAT?
A:

Important formulas are Area of Circle (πr²), Circumference (2πr), and Pythagoras theorem (a² + b² = c²). Triangle area ½ × base × height and Volume of Cylinder (πr²h) are also common. CAT Geometry questions depend directly on these.

Q: Are there important formulas in Number System for CAT?
A:

Yes, formulas like LCM × HCF = Product of numbers and sum of series are important. Examples: sum of first n natural numbers n(n+1)/2 and squares n(n+1)(2n+1)/6. Divisibility rules also save time in CAT questions.

Q: Can I prepare for CAT 2025 without coaching?
A:

Absolutely. Many aspirants successfully prepare using self-study materials, previous year papers, and practice tests. Discipline and a well-structured study plan are key to self-preparation.

Q: Do I need to remember all formulas for CAT 2025?
A:

You don’t need every formula ever made—just focus on those repeatedly asked in previous CAT papers. Prioritise core areas like Arithmetic, Algebra, and Geometry for best results.

Q: How can I memorise CAT formulas effectively?
A:

Write formulas in a separate notebook or digital sheet, revise them daily, and practise topic-wise questions. Repetition through mock tests helps build long-term memory and faster recall during the exam.

Q: How does a CAT formula sheet help in exam preparation?
A:

A well-organised CAT formula sheet saves revision time, prevents confusion, and improves problem-solving speed. It’s especially useful for last-minute revision before mocks and the final CAT exam.

Q: Where can I find topic-wise CAT 2025 formulas?
A:

You can create your own sheet from trusted CAT preparation books or refer to online resources like Careers360 and coaching material that list CAT 2025 topic-wise formulas for quick reference.

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Questions related to CAT

On Question asked by student community

Have a question related to CAT ?

Hi there,

The minimum eligibility criteria for a general candidate to receive a call from IIM Sambalpur are as follows:
VARC: 65%ile
QUANTS: 65%ile
LRDI: 65%ile
Overall: 90%tile
Keep practising and aim to improve your score. You can also focus on other management exams where you may secure a strong

Hi there,

With a B.tech in industrial engineering from IIT Roorkee and a CAT 2025 score of 98.89 percentile and strong sectionals your profile is solid for top B-schools. For the top IIMs like Ahmedabad and Bangalore, calls for engineers usually go to candidates with near perfect percentiles. Your score

Hello,
The IIT Guwahati cutoff for SC and EWS categories depends on the branch, year, and JoSAA counselling round, but you can get a general idea from recent trends.

For the SC category, closing ranks usually range from 4,000 to 9,000 for popular branches like CSE, ECE, and Mechanical, while

with this percentile, you can get into tier 2 or tier 3 college, the list of the few notable college is given below-

1) FLAME university, Pune

2) AIMS institute, Bangalore

3) Doon business school, Dehradun

4) Christ university, Bangalore

5) NIT Trichy

6) KIIT school of management, Bhuvneshwar






A CAT percentile of 99.64 is an excellent score and definitely places you in a strong position for top IIM calls, including IIM Ahmedabad, IIM Bangalore, and IIM Calcutta. However, admission to these institutes is not based on CAT score alone. Each of these IIMs follows a holistic selection process